Question: Solve for $x$ and $y$ using substitution. ${-6x-6y = -6}$ ${y = 3x-11}$
Solution: Since $y$ has already been solved for, substitute $3x-11$ for $y$ in the first equation. ${-6x - 6}{(3x-11)}{= -6}$ Simplify and solve for $x$ $-6x-18x + 66 = -6$ $-24x+66 = -6$ $-24x+66{-66} = -6{-66}$ $-24x = -72$ $\dfrac{-24x}{{-24}} = \dfrac{-72}{{-24}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {y = 3x-11}\thinspace$ to find $y$ ${y = 3}{(3)}{ - 11}$ $y = 9 - 11$ $y = -2$ You can also plug ${x = 3}$ into $\thinspace {-6x-6y = -6}\thinspace$ and get the same answer for $y$ : ${-6}{(3)}{ - 6y = -6}$ ${y = -2}$